Gesture in Mental Abacus Calculation

1 University of Chicago, 2 University of California-San Diego, 3 Stanford University

Wherever we go, we take with us a pair of very powerful tools for thinking, learning, and communicating about spatial information: our hands. Over the past few decades, scientific evidence has accumulated showing that the ways that people move their hands not only reflects the ways that they’re thinking about problems (e.g. Church & Goldin-Meadow, 1986; Alibali & Goldin-Meadow, 1993; Pine, Lufkin, & Messer, 2004), but can actively change learning and performance outcomes. For example, encouraging children to gesture when explaining their answers to math problems prior to a math lesson significantly improves their ability to profit from that lesson (Broaders, Cook, Mitchell, & Goldin-Meadow, 2007).

The fact that the hands can be used as a learning tool has powerful implications for education. However, in order to design effective classroom interventions we need to understand the mechanisms by which gestures can influence thought. Does gesture influence thought by supporting specific cognitive processes such as mental imagery, or by facilitating associations between the motor system and more abstract conceptual information?

Gaining a better understanding of these mechanisms would have broad theoretical implications: it would provide insight into how humans represent both concrete and more abstract spatial information and into the ways that distinct cognitive processes interact in allowing us to reason and learn about challenging concepts. Critically, this knowledge would also lead to a better understanding of how gestures can be used by teachers and students to facilitate learning, especially in spatially rich content areas like chemistry and physics.

There are, however, large challenges to determining the role that gestures play in cognition. Chief among them is that when people gesture, they typically speak at the same time. In an experimental setting, it is difficult to separate the effects that gesture has on learning from the effects of the accompanying talk. Moreover, gestures produced along with speech have the added burden of communicating information to a conversation partner. The challenge is to pull apart the role gesture plays in learning from its role in communication.

In this project, we study the ways that gesture and cognition interact in a setting where gestures are produced in the absence of speech and in a non-communicative context: problem solving on a mental abacus. Mental abacus is a method of doing arithmetic by imagining the movements of beads on an abacus; it is a technique learned by many students around the world, particularly in Asia. Students typically begin by learning to use the abacus as a computational tool, and then learn to solve problems without a physical abacus present. The video below shows a student adding up ten 2-digit addends in about 6 seconds:

58

99

52

12

78

40

61

46

86

+ 41

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Even though the child in the video is not physically moving the beads on an abacus, he is moving his hands in ways that are consistent with making bead movements. Of the over 200 Mental Abacus users that we have tested, all have spontaneously used their hands in this manner.

As a first step to understanding the gestures of Mental Abacus users, we undertook a study to observe children’s gestures and investigate how they were related to math performance. Our participants were 86 children studying Mental Abacus in afterschool programs in Gujarat Province, India. We videotaped them solving arithmetic problems of varying difficulty, and also measured their performance on a math task on which they were not permitted to gesture. We measured performance on the math task with and without gesture in order to assess the children’s dependence on gesture.

We found a great deal of variability in how dependent children were on their gestures. Overall, children performed 26% worse when they were not allowed to gesture than when gesture was permitted, but the range across children was large: some children did equally well with and without gesture, others did as much as 80% worse when they were not permitted to gesture than when gesture was permitted.

Although all children gestured on almost every problem, the size of the children’s gestures varied quite a bit. In some cases, children’s movements were very slight, smaller than the physical abacuses on which they were trained. In other cases, children would perform their movements with their whole arms, moving their hands as high as their heads. To determine whether these differences in gesture size related to math performance, we coded the size of the gestures on each trial on a four-point scale, from smaller than a physical abacus to large enough to require large-scale movement of the arms (beyond the wrists and fingers). See below for examples of each gesture size.

Was this variation in gesture size related to the demands of the task? If gesture is actively contributing to performance on the math task, we might expect gesture size to vary as a function of the difficulty of the problem. To test this hypothesis, we calculated the difficulty of each problem for each individual child: for some children, adding 5 addends was very challenging, whereas for others, adding 9 or 10 addends was relatively easy. We gave each of the problems a child solved a difficulty score, and examined the size of the gestures that the child produced at that difficulty level. The results showed a striking increase in average gesture size as problems became more and more difficult:

This finding is striking because it suggests that the size of a child’s gestures are not a character trait; rather, children appear to flexibly adjust the size of their gestures depending on how difficult the problem they are solving is.

Does this size adjustment in gesture help children solve more difficult problems? Research has shown that the size of an imagined mental image can affect how detailed it is, and perhaps also its accuracy (Kosslyn, 1976;Thompson, Hsiao, & Kosslyn, 2011). To determine whether the same is true of gesture size on the abacus task, we instructed children to produce large and small gestures on problems that were matched for difficulty. We are currently investigating whether children’s math performance was affected by this manipulation.

Even if it turns out that gesture size does not play a functional role for the child, gesture size might still reflect how much the child is relying on gesture. To explore this possibility, we compared children’s average gesture size on problems that were moderately difficult for them to the children’s decline in math performance when they were not allowed to gesture. We found a moderate correlation between a child’s gesture size and the degree to which their performance declined when they were not permitted to gesture, suggesting that children who habitually produce larger gestures may also rely more heavily on gesture and, as a result, suffer when not permitted to gesture. Although more work is needed, this finding is consistent with the idea that when gestures are larger, they are playing a larger role in children’s cognition.

Together, these findings provide evidence that gesture is actively contributing to children’s performance on mental abacus tasks. In addition, they inform our hypotheses about the roles gesture could be playing in cognition. The fact that gesture size is a flexible predictor of problem difficulty requires further investigation into whether gesture and mental imagery size similarly affect performance, and into the degree to which gesture and mental imagery might be related. However, the fact that children gesture even on very easy problems suggests that gesture may serve some function even on very easy problems. One possibility is that gestures play a role in recalling specific mental abacus procedures, which were needed even on the easiest problems we presented. In future studies planned for this spring, we plan to address two primary hypotheses: first, whether gesture directly supports a visual representation of bead locations on the abacus; and second, whether gesture helps students to represent or remember specific procedures for acting on the abacus.